Subgroups — #26238782

Order 12032.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252843	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689237	C₂	1	2	yes	maximal, complemented
3	#20252134	C₂	1	1	yes	maximal, characteristic, complemented
4	#20251956	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244216	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244163	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244093	C₂	1	2	yes	maximal, complemented
8	#20243713	C₂	1	2	yes	maximal, complemented
9	#20243664	C₂	1	2	yes	maximal, complemented
10	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#104×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094044	C₂²	1	2	yes	—
13	C₂×#13094032	C₂²	1	2	yes	—
14	C₂×#13094031	C₂²	1	2	yes	—
15	#15689673	C₂²	1	1	yes	characteristic
16	#15689345	C₄	1	2	yes	complemented
17	#15689338	C₄	1	2	yes	complemented
18	#15689333	C₄	1	1	yes	characteristic, complemented
19	#15689328	C₄	1	1	yes	characteristic, complemented
20	#15689323	C₄	1	1	yes	characteristic, complemented
21	#15689318	C₄	1	1	yes	characteristic, complemented
22	#15689237	—	2	8	no	—
23	#15689202	—	2	1	no	—
24	#15689196	—	2	2	no	—
25	C₈×D₁₈₈	—	2	1	no	—
26	C₂×#13093959	C₂²	1	2	yes	—
27	#15689150	—	2	2	no	—
28	#15689150	C₂²	1	2	yes	—
29	#15689147	—	2	1	no	—
30	#15689147	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
32	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×#13093952	C₂²	1	2	yes	—
35	C₂×#13093952	C₂²	1	2	yes	—
36	#15689117	C₂²	1	2	yes	—
37	#15689091	C₂²	1	2	yes	—
38	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
39	#15688887	C₂²	1	2	yes	—
40	#15688878	C₂²	1	2	yes	—
41	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#104×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#104×C₄₇	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
45	C₄³×C₄₇	C₂²	1	1	yes	characteristic
46	C₄₇×#339	C₂²	1	1	yes	characteristic
47	C₄₇×#339	C₂²	1	1	yes	characteristic
48	C₂×#10625350	C₂³	1	2	yes	—
49	#13094044	—	2	4	no	—
50	#13094044	—	2	4	no	—
51	C₂×#10625337	C₂×C₄	1	2	yes	—
52	C₂×#10625335	C₂×C₄	1	2	yes	—
53	C₂×#10625336	C₂×C₄	1	2	yes	—
54	C₂×#10625334	C₂×C₄	1	2	yes	—
55	#13094032	—	2	4	no	—
56	#13094032	—	4	2	no	—
57	#13094031	—	2	4	no	—
58	#13094031	—	4	2	no	—
59	C₂×#10625329	—	2	2	no	—
60	C₂×#10625329	C₂³	1	2	yes	—
61	C₂×#10625324	—	2	2	no	—
62	C₂²×C₄₇⋊C₈	—	2	2	no	—
63	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
64	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
65	C₂×C₈×D₄₇	—	2	2	no	—
66	#13094024	C₂×C₄	1	1	yes	characteristic
67	#13094021	C₂×C₄	1	1	yes	characteristic
68	#13094012	C₂×C₄	1	2	yes	—
69	#13093998	—	2	1	no	—
70	#13093998	—	2	1	no	—
71	C₄×D₁₈₈	—	2	1	no	—
72	C₄×D₁₈₈	—	2	1	no	—
73	#13093959	—	2	4	no	—
74	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
75	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
76	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
77	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
78	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
79	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
81	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
82	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
83	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
84	#13093952	—	2	4	no	—
85	#13093952	—	4	2	no	—
86	#13093947	C₂×C₄	1	2	yes	—
87	#13093947	C₂×C₄	1	2	yes	—
88	#13093944	C₂×C₄	1	2	yes	—
89	#13093944	C₂×C₄	1	2	yes	—
90	(C₂×D₄₇)⋊C₈	—	2	2	no	—
91	(C₂×D₄₇)⋊C₈	—	2	2	no	—
92	C₄×C₄₇⋊C₈	—	2	4	no	—
93	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₄×D₄×C₄₇	—	2	1	no	—
99	C₄×D₄×C₄₇	—	2	1	no	—
100	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
101	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
102	#117×C₄₇	—	2	1	no	—
103	#117×C₄₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	—	2	1	no	—
105	C₂×C₄²×C₄₇	—	2	1	no	—
106	C₂×C₄²×C₄₇	—	2	1	no	—
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	#104×C₄₇	—	2	2	no	—
111	#104×C₄₇	D₄	1	4	yes	complemented
112	#97×C₄₇	—	2	1	no	—
113	C₄×C₈×C₄₇	—	2	1	no	—
114	#41×C₄₇	—	2	1	no	—
115	#41×C₄₇	—	2	1	no	—
116	#41×C₄₇	C₂×D₄	1	2	yes	—
117	#41×C₄₇	#41	1	2	yes	—
118	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₄×C₄₇	—	2	1	no	—
120	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
129	C₂×C₂²⋊D₄₇	—	2	2	no	—
130	#10625350	—	2	2	no	—
131	#10625350	—	2	2	no	—
132	#10625350	—	2	2	no	—
133	#10625350	—	2	2	no	—
134	C₂×D₁₈₈	—	2	1	no	—
135	C₂×D₁₈₈	—	2	1	no	—
136	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
137	C₂×C₄×D₄₇	—	2	2	no	—
138	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
139	M₁₆×C₄₇	—	2	1	no	—
140	M₁₆×C₄₇	—	2	1	no	—
141	M₁₆×C₄₇	—	2	1	no	—
142	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₄₇	—	2	1	no	—
144	C₂×C₈×C₄₇	—	2	1	no	—
145	C₄⋊C₄×C₄₇	—	2	1	no	—
146	C₄⋊C₄×C₄₇	—	2	1	no	—
147	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₄₇	—	2	1	no	—
150	C₂²⋊C₄×C₄₇	—	2	1	no	—
151	C₂²⋊C₄×C₄₇	—	2	1	no	—
152	C₄²×C₄₇	—	2	4	no	—
153	C₄²×C₄₇	—	2	1	no	—
154	C₄²×C₄₇	—	2	1	no	—
155	C₄²×C₄₇	—	2	1	no	—
156	C₄²×C₄₇	—	2	1	no	—
157	C₄²×C₄₇	—	2	1	no	—
158	C₄²×C₄₇	—	2	1	no	—
159	C₄²×C₄₇	—	4	2	no	—
160	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₄₇	C₂×D₄	1	2	yes	—
163	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
165	#10625337	—	2	4	no	—
166	#10625336	—	2	4	no	—
167	#10625335	—	2	4	no	—
168	#10625334	—	2	4	no	—
169	(C₂×D₄₇)⋊C₄	—	2	2	no	—
170	(C₂×D₄₇)⋊C₄	—	2	2	no	—
171	C₄⋊Dic₄₇	—	2	1	no	—
172	C₄⋊Dic₄₇	—	2	1	no	—
173	#10625329	—	2	2	no	—
174	#10625329	—	2	2	no	—
175	#10625329	—	4	4	no	—
176	C₂×C₄₇⋊C₈	—	2	2	no	—
177	C₂×C₄₇⋊C₈	—	2	2	no	—
178	C₂×C₄₇⋊C₈	—	2	2	no	—
179	C₂×C₄₇⋊C₈	—	2	2	no	—
180	C₂×C₄₇⋊C₈	—	2	2	no	—
181	C₂×C₄₇⋊C₈	—	4	4	no	—
182	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
183	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
184	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
185	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
186	#10625324	—	4	4	no	—
187	C₈×D₄₇	—	4	4	no	—
188	C₂³×C₄₇	—	2	1	no	—
189	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
190	C₂²×D₄₇	—	2	2	no	—
191	Q₈×C₄₇	—	2	1	no	—
192	Q₈×C₄₇	C₄×D₄	1	2	yes	—
193	D₄×C₄₇	—	2	2	no	—
194	D₄×C₄₇	—	2	2	no	—
195	D₄×C₄₇	—	2	1	no	—
196	D₄×C₄₇	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	1	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	1	no	—
206	C₂×C₄×C₄₇	—	2	1	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	—	8	1	no	—
212	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
222	C₂²⋊D₄₇	—	4	2	no	—
223	C₂²⋊D₄₇	—	4	2	no	—
224	C₂×Dic₄₇	—	2	2	no	—
225	D₁₈₈	—	2	2	no	—
226	D₁₈₈	—	2	2	no	—
227	D₁₈₈	—	4	2	no	—
228	D₁₈₈	—	8	1	no	—
229	C₄×D₄₇	—	4	2	no	—
230	C₄×D₄₇	—	4	2	no	—
231	Dic₉₄	—	2	2	no	—
232	Dic₉₄	—	2	2	no	—
233	C₈×C₄₇	—	2	2	no	—
234	C₈×C₄₇	—	4	1	no	—
235	C₄₇⋊C₈	—	2	2	no	—
236	C₄₇⋊C₈	—	2	2	no	—
237	C₄₇⋊C₈	—	2	2	no	—
238	C₄₇⋊C₈	—	2	2	no	—
239	C₄₇⋊C₈	—	4	2	no	—
240	#23015	—	47	1	no	maximal, Sylow
241	C₂²×C₄₇	—	2	1	no	—
242	C₂²×C₄₇	—	2	1	no	—
243	C₂²×C₄₇	—	2	2	no	—
244	C₂²×C₄₇	—	4	1	no	—
245	C₂²×C₄₇	—	4	1	no	—
246	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₄₇	#547	1	1	yes	characteristic
248	C₂²×C₄₇	#553	1	1	yes	characteristic
249	C₂×D₄₇	—	4	2	no	—
250	C₂×D₄₇	—	4	2	no	—
251	C₂×D₄₇	—	4	2	no	—
252	C₄×C₄₇	—	2	4	no	—
253	C₄×C₄₇	—	2	2	no	—
254	C₄×C₄₇	—	2	1	no	—
255	C₄×C₄₇	—	2	1	no	—
256	C₄×C₄₇	—	2	1	no	—
257	C₄×C₄₇	—	4	2	no	—
258	C₄×C₄₇	—	4	1	no	—
259	C₄×C₄₇	—	4	1	no	—
260	C₄×C₄₇	#443	1	2	yes	complemented
261	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
262	C₄×C₄₇	#520	1	1	yes	characteristic
263	C₄×C₄₇	D₄²	1	1	yes	characteristic
264	C₄×C₄₇	#548	1	1	yes	characteristic
265	Dic₄₇	—	4	2	no	—
266	#3035	—	47	1	no	—
267	C₂×#443	—	47	2	no	—
268	#2935	—	47	1	no	—
269	#2906	—	47	1	no	—
270	#1962	—	47	1	no	—
271	#1950	—	47	1	no	—
272	#1937	—	47	2	no	—
273	#1876	—	47	2	no	—
274	#1866	—	47	2	no	—
275	C₄×C₄⋊C₈	—	47	1	no	—
276	C₄×#104	D₄₇	1	1	yes	characteristic, complemented
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	2	1	no	—
279	C₂×C₄₇	—	4	2	no	—
280	C₂×C₄₇	#2361	1	1	yes	characteristic
281	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
282	C₂×C₄₇	#2956	1	1	yes	characteristic
283	D₄₇	—	8	2	no	—
284	C₂×#135	—	47	2	no	—
285	C₂×#131	—	47	2	no	—
286	C₂×#131	—	47	2	no	—
287	#532	—	47	1	no	—
288	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
289	#464	—	47	2	no	—
290	#463	—	47	2	no	—
291	#462	—	47	1	no	—
292	#461	—	47	1	no	—
293	#460	—	47	1	no	—
294	#459	—	47	1	no	—
295	#443	—	94	8	no	—
296	#436	—	94	1	no	—
297	#435	—	94	2	no	—
298	C₈×D₄	—	94	1	no	—
299	C₂×#108	—	47	2	no	—
300	#424	—	47	2	no	—
301	#424	—	94	2	no	—
302	#423	—	47	1	no	—
303	#423	—	94	1	no	—
304	C₂×C₄⋊C₈	—	47	1	no	—
305	C₂×C₄⋊C₈	—	47	1	no	—
306	C₂×C₄⋊C₈	—	94	1	no	—
307	C₂×#104	—	47	2	no	—
308	C₂×#104	—	47	2	no	—
309	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
310	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
311	#416	—	47	2	no	—
312	#408	—	47	2	no	—
313	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
314	C₂×C₄×C₈	—	47	2	no	—
315	C₄³	C₂×D₄₇	1	1	yes	characteristic
316	#341	—	47	2	no	—
317	#339	C₂×D₄₇	1	1	yes	characteristic
318	#339	C₂×D₄₇	1	1	yes	characteristic
319	#336	—	47	2	no	—
320	C₄₇	#23015	1	1	yes	characteristic, complemented, Sylow
321	C₂×#41	—	47	2	no	—
322	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
323	#135	—	94	4	no	—
324	#135	—	94	4	no	—
325	C₂×Q₁₆	—	47	2	no	—
326	C₂×SD₁₆	—	47	2	no	—
327	C₂×SD₁₆	—	47	2	no	—
328	C₂×D₈	—	47	2	no	—
329	#131	—	94	4	no	—
330	#131	—	94	4	no	—
331	#131	—	188	2	no	—
332	#131	—	188	2	no	—
333	C₂×M₁₆	—	47	2	no	—
334	C₂×M₁₆	—	94	2	no	—
335	C₂×M₁₆	—	94	2	no	—
336	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
337	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
338	C₂²×C₈	—	47	2	no	—
339	C₂²×C₈	—	47	2	no	—
340	C₂²×C₈	—	94	2	no	—
341	C₂²×C₈	—	94	2	no	—
342	C₄⋊Q₈	—	47	1	no	—
343	#127	—	47	1	no	—
344	#124	—	47	2	no	—
345	#121	—	94	1	no	—
346	#121	—	94	1	no	—
347	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
348	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	94	1	no	—
352	C₄×D₄	—	94	1	no	—
353	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
354	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
355	#117	—	2	1	no	—
356	#117	C₂²×D₄₇	1	1	yes	characteristic
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
361	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
362	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
363	#108	—	94	4	no	—
364	C₄⋊C₈	—	47	1	no	—
365	C₄⋊C₈	—	47	1	no	—
366	C₄⋊C₈	—	47	2	no	—
367	C₄⋊C₈	—	47	1	no	—
368	C₄⋊C₈	—	47	1	no	—
369	C₄⋊C₈	—	47	2	no	—
370	C₄⋊C₈	—	94	2	no	—
371	C₄⋊C₈	—	94	2	no	—
372	C₄⋊C₈	—	94	1	no	—
373	C₄⋊C₈	—	94	1	no	—
374	#104	—	2	2	no	—
375	#104	—	94	4	no	—
376	#104	—	188	2	no	—
377	#104	D₁₈₈	1	4	yes	complemented
378	#103	—	47	2	no	—
379	#103	—	47	2	no	—
380	#102	—	47	2	no	—
381	#102	—	47	2	no	—
382	C₂²⋊C₈	—	94	2	no	—
383	C₂²⋊C₈	—	94	2	no	—
384	#97	—	2	1	no	—
385	C₄×C₈	—	2	1	no	—
386	C₄×C₈	—	94	4	no	—
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	94	2	no	—
390	#41	—	94	2	no	—
391	#41	—	94	2	no	—
392	#41	—	94	2	no	—
393	#41	C₂×D₁₈₈	1	2	yes	—
394	#41	#10625350	1	2	yes	—
395	C₂×Q₈	—	47	2	no	—
396	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	47	2	no	—
399	C₂×D₄	—	94	2	no	—
400	C₂×D₄	—	94	1	no	—
401	C₂×D₄	—	94	1	no	—
402	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	94	2	no	—
409	C₂²×C₄	#10625352	1	1	yes	characteristic
410	C₂²×C₄	#10625352	1	1	yes	characteristic
411	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
412	Q₁₆	—	94	4	no	—
413	SD₁₆	—	94	4	no	—
414	SD₁₆	—	94	4	no	—
415	D₈	—	94	4	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	94	2	no	—
420	M₁₆	—	94	2	no	—
421	M₁₆	—	188	4	no	—
422	M₁₆	—	188	4	no	—
423	M₁₆	C₂×D₁₈₈	1	2	yes	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	47	2	no	—
427	C₂×C₈	—	47	2	no	—
428	C₂×C₈	—	47	2	no	—
429	C₂×C₈	—	47	2	no	—
430	C₂×C₈	—	94	2	no	—
431	C₂×C₈	—	94	2	no	—
432	C₂×C₈	—	94	2	no	—
433	C₂×C₈	—	94	2	no	—
434	C₂×C₈	—	94	2	no	—
435	C₂×C₈	—	188	4	no	—
436	C₂×C₈	—	188	4	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	94	1	no	—
440	C₄⋊C₄	—	94	1	no	—
441	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
442	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	94	2	no	—
447	C₂²⋊C₄	—	94	2	no	—
448	C₄²	—	2	4	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	4	2	no	—
456	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
457	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
458	C₄²	C₂×D₁₈₈	1	2	yes	—
459	C₄²	D₄×D₄₇	1	1	yes	characteristic
460	C₄²	D₄×D₄₇	1	1	yes	characteristic
461	C₂³	—	2	1	no	—
462	C₂³	—	94	2	no	—
463	C₂³	C₂×#10625352	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	94	2	no	—
466	Q₈	—	94	2	no	—
467	Q₈	C₄×D₁₈₈	1	2	yes	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	1	no	—
471	D₄	—	94	2	no	—
472	D₄	—	94	2	no	—
473	D₄	—	376	1	no	—
474	D₄	—	188	2	no	—
475	D₄	—	188	2	no	—
476	D₄	—	188	2	no	—
477	D₄	C₄×D₁₈₈	1	2	yes	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	8	1	no	—
493	C₂×C₄	—	94	2	no	—
494	C₂×C₄	—	188	2	no	—
495	C₂×C₄	—	188	2	no	—
496	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
497	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
498	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
499	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
500	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
501	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
503	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
504	C₂×C₄	#13094070	1	1	yes	characteristic
505	C₂×C₄	#13094071	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	4	1	no	—
508	C₈	—	94	2	no	—
509	C₈	—	94	2	no	—
510	C₈	—	94	2	no	—
511	C₈	—	94	2	no	—
512	C₈	—	188	2	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	188	2	no	—
519	C₂²	—	188	2	no	—
520	C₂²	—	188	2	no	—
521	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
522	C₂²	#15689777	1	1	yes	characteristic
523	C₂²	#15689819	1	1	yes	characteristic
524	C₄	—	2	4	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	188	2	no	—
533	C₄	#15689237	1	2	yes	complemented
534	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
535	C₄	#15689603	1	1	yes	characteristic
536	C₄	D₄×D₁₈₈	1	1	yes	characteristic
537	C₄	#15689782	1	1	yes	characteristic
538	C₂	—	2	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	4	2	no	—
541	C₂	—	376	2	no	—
542	C₂	#20246402	1	1	yes	characteristic
543	C₂	C₂×#15689237	1	1	yes	characteristic
544	C₂	#20252294	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#104×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252843	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#104	D₄₇
hypocenter	C₄₇	#23015
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#104

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#15689237	C₂	semidirect
3. #20252134	C₂	semidirect
4. #20251956	C₂	semidirect
5. #20244216	C₂	semidirect
6. #20244163	C₂	semidirect
7. #20244093	C₂	semidirect
8. #20243713	C₂	semidirect
9. #20243664	C₂	semidirect
10. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
11. C₄×#104×C₄₇	C₂	semidirect
16. #15689345	C₄	semidirect
17. #15689338	C₄	semidirect
18. #15689333	C₄	semidirect
19. #15689328	C₄	semidirect
20. #15689323	C₄	semidirect
21. #15689318	C₄	semidirect
111. #104×C₄₇	D₄	semidirect
260. C₄×C₄₇	#443	semidirect
276. C₄×#104	D₄₇	semidirect
320. C₄₇	#23015	semidirect
377. #104	D₁₈₈	semidirect
533. C₄	#15689237	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20252843	2
C₂×#15689237	2
#20252134	2
#20251956	2
#20244216	2
#20244163	2
#20244093	2
#20243713	2
#20243664	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×#104×C₄₇	2
#23015	47